Necessary optimality conditions for bilevel set optimization problems

被引：22
|
作者：
Dempe, S.
Gadhi, N.
机构：
[1] Sidi Mohamed Ben Abdellah Univ, Dept Math, Fes, Morocco
[2] Tech Univ Bergakademie Freiberg, Dept Math & Comp Sci, Freiberg, Germany
来源：
JOURNAL OF GLOBAL OPTIMIZATION | 2007年 / 39卷 / 04期
关键词：
Bilevel optimization; convexificator; Karush-Kuhn-Tucker multipliers; necessary Optimality conditions; regularity condition; set valued mappings; support function;
D O I：
10.1007/s10898-007-9154-0
中图分类号：
C93 [管理学]; O22 [运筹学];
学科分类号：
070105 ; 12 ; 1201 ; 1202 ; 120202 ;
摘要：
Bilevel programming problems are hierarchical optimization problems where in the upper level problem a function is minimized subject to the graph of the solution set mapping of the lower level problem. In this paper necessary optimality conditions for such problems are derived using the notion of a convexificator by Luc and Jeyakumar. Convexificators are subsets of many other generalized derivatives. Hence, our optimality conditions are stronger than those using e.g., the generalized derivative due to Clarke or Michel-Penot. Using a certain regularity condition Karush-Kuhn-Tucker conditions are obtained.
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页码：529 / 542
页数：14
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